Face verification remains a challenging problem in very complex conditions with large variations such as pose, illumination, expression, and occlusions. This problem is exacerbated when we rely unrealistically on a single training data source, which is often insufficient to cover the intrinsically complex face variations. This paper proposes a principled multi-task learning approach based on Discriminative Gaussian Process Latent Variable Model, named GaussianFace, to enrich the diversity of training data. In comparison to existing methods, our model exploits additional data from multiple source-domains to improve the generalization performance of face verification in an unknown target-domain. Importantly, our model can adapt automatically to complex data distributions, and therefore can well capture complex face variations inherent in multiple sources. Extensive experiments demonstrate the effectiveness of the proposed model in learning from diverse data sources and generalize to unseen domain. Specifically, the accuracy of our algorithm achieves an impressive accuracy rate of 98.52% on the well-known and challenging Labeled Faces in the Wild (LFW) benchmark [23]. For the first time, the human-level performance in face verification (97.53%) [28] on LFW is surpassed.

Detecting faults in electrical power grids is of paramount importance, either from the electricity operator and consumer viewpoints. Modern electric power grids (smart grids) are equipped with smart sensors that allow to gather real-time information regarding the physical status of all the component elements belonging to the whole infrastructure (e.g., cables and related insulation, transformers, breakers and so on). In real-world smart grid systems, usually, additional information that are related to the operational status of the grid itself are collected such as meteorological information. Designing a suitable recognition (discrimination) model of faults in a real-world smart grid system is hence a challenging task. This follows from the heterogeneity of the information that actually determine a typical fault condition. The second point is that, for synthesizing a recognition model, in practice only the conditions of observed faults are usually meaningful. Therefore, a suitable recognition model should be synthesized by making use of the observed fault conditions only. In this paper, we deal with the problem of modeling and recognizing faults in a real-world smart grid system, which supplies the entire city of Rome, Italy. Recognition of faults is addressed by following a combined approach of multiple dissimilarity measures customization and one-class classification techniques. We provide here an in-depth study related to the available data and to the models synthesized by the proposed one-class classifier. We offer also a comprehensive analysis of the fault recognition results by exploiting a fuzzy set based reliability decision rule.

For the problem of binary linear classification and feature selection, we propose algorithmic approaches to classifier design based on the generalized approximate message passing (GAMP) algorithm, recently proposed in the context of compressive sensing. We are particularly motivated by problems where the number of features greatly exceeds the number of training examples, but where only a few features suffice for accurate classification. We show that sum-product GAMP can be used to (approximately) minimize the classification error rate and max-sum GAMP can be used to minimize a wide variety of regularized loss functions. Furthermore, we describe an expectation-maximization (EM)-based scheme to learn the associated model parameters online, as an alternative to cross-validation, and we show that GAMP's state-evolution framework can be used to accurately predict the misclassification rate. Finally, we present a detailed numerical study to confirm the accuracy, speed, and flexibility afforded by our GAMP-based approaches to binary linear classification and feature selection.

To estimate a sparse linear model from data with Gaussian noise, consilience from lasso and compressed sensing literatures is that thresholding estimators like lasso and the Dantzig selector have the ability in some situations to identify with high probability part of the significant covariates asymptotically, and are numerically tractable thanks to convexity. Yet, the selection of a threshold parameter $\lambda$ remains crucial in practice. To that aim we propose Quantile Universal Thresholding, a selection of $\lambda$ at the detection edge. We show with extensive simulations and real data that an excellent compromise between high true positive rate and low false discovery rate is achieved, leading also to good predictive risk.

We expand the item response theory to study the case of "cheating students" for a set of exams, trying to detect them by applying a greedy algorithm of inference. This extended model is closely related to the Boltzmann machine learning. In this paper we aim to infer the correct biases and interactions of our model by considering a relatively small number of sets of training data. Nevertheless, the greedy algorithm that we employed in the present study exhibits good performance with a few number of training data. The key point is the sparseness of the interactions in our problem in the context of the Boltzmann machine learning: the existence of cheating students is expected to be very rare (possibly even in real world). We compare a standard approach to infer the sparse interactions in the Boltzmann machine learning to our greedy algorithm and we find the latter to be superior in several aspects.

When the design matrix has orthonormal columns, "soft thresholding" the ordinary least squares (OLS) solution produces the Lasso solution [Tibshirani, 1996]. If one uses the Puffer preconditioned Lasso [Jia and Rohe, 2012], then this result generalizes from orthonormal designs to full rank designs (Theorem 1). Theorem 2 refines the Puffer preconditioner to make the Lasso select the same model as removing the elements of the OLS solution with the largest p-values. Using a generalized Puffer preconditioner, Theorem 3 relates ridge regression to the preconditioned Lasso; this result is for the high dimensional setting, p > n. Where the standard Lasso is akin to forward selection [Efron et al., 2004], Theorems 1, 2, and 3 suggest that the preconditioned Lasso is more akin to backward elimination. These results hold for sparse penalties beyond l1; for a broad class of sparse and non-convex techniques (e.g. SCAD and MC+), the results hold for all local minima.

Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current literature is split into two kinds of tests - those which are consistent without any assumptions about how the distributions may differ (\textit{general} alternatives), and those which are designed to specifically test easier alternatives, like a difference in means (\textit{mean-shift} alternatives). The main contribution of this paper is to explicitly characterize the power of a popular nonparametric two sample test, designed for general alternatives, under a mean-shift alternative in the high-dimensional setting. Specifically, we explicitly derive the power of the linear-time Maximum Mean Discrepancy statistic using the Gaussian kernel, where the dimension and sample size can both tend to infinity at any rate, and the two distributions differ in their means. As a corollary, we find that if the signal-to-noise ratio is held constant, then the test's power goes to one if the number of samples increases faster than the dimension increases. This is the first explicit power derivation for a general nonparametric test in the high-dimensional setting, and also the first analysis of how tests designed for general alternatives perform when faced with easier ones.

According to Cobanoglu et al and Murphy, it is now widely acknowledged that the single target paradigm (one protein or target, one disease, one drug) that has been the dominant premise in drug development in the recent past is untenable. More often than not, a drug-like compound (ligand) can be promiscuous - that is, it can interact with more than one target protein. In recent years, in in silico target prediction methods the promiscuity issue has been approached computationally in different ways. In this study we confine attention to the so-called ligand-based target prediction machine learning approaches, commonly referred to as target-fishing. With a few exceptions, the target-fishing approaches that are currently ubiquitous in cheminformatics literature can be essentially viewed as single-label multi-classification schemes; these approaches inherently bank on the single target paradigm assumption that a ligand can home in on one specific target. In order to address the ligand promiscuity issue, one might be able to cast target-fishing as a multi-label multi-class classification problem. For illustrative and comparison purposes, single-label and multi-label Naive Bayes classification models (denoted here by SMM and MMM, respectively) for target-fishing were implemented. The models were constructed and tested on 65,587 compounds and 308 targets retrieved from the ChEMBL17 database. SMM and MMM performed differently: for 16,344 test compounds, the MMM model returned recall and precision values of 0.8058 and 0.6622, respectively; the corresponding recall and precision values yielded by the SMM model were 0.7805 and 0.7596, respectively. However, at a significance level of 0.05 and one degree of freedom McNemar test performed on the target prediction results returned by SMM and MMM for the 16,344 test ligands gave a chi-squared value of 15.656, in favour of the MMM approach.

In this paper, we consider the matrix completion problem when the observations are one-bit measurements of some underlying matrix M, and in particular the observed samples consist only of ones and no zeros. This problem is motivated by modern applications such as recommender systems and social networks where only "likes" or "friendships" are observed. The problem of learning from only positive and unlabeled examples, called PU (positive-unlabeled) learning, has been studied in the context of binary classification. We consider the PU matrix completion problem, where an underlying real-valued matrix M is first quantized to generate one-bit observations and then a subset of positive entries is revealed. Under the assumption that M has bounded nuclear norm, we provide recovery guarantees for two different observation models: 1) M parameterizes a distribution that generates a binary matrix, 2) M is thresholded to obtain a binary matrix. For the first case, we propose a "shifted matrix completion" method that recovers M using only a subset of indices corresponding to ones, while for the second case, we propose a "biased matrix completion" method that recovers the (thresholded) binary matrix. Both methods yield strong error bounds --- if M is n by n, the Frobenius error is bounded as O(1/((1-rho)n), where 1-rho denotes the fraction of ones observed. This implies a sample complexity of O(n\log n) ones to achieve a small error, when M is dense and n is large. We extend our methods and guarantees to the inductive matrix completion problem, where rows and columns of M have associated features. We provide efficient and scalable optimization procedures for both the methods and demonstrate the effectiveness of the proposed methods for link prediction (on real-world networks consisting of over 2 million nodes and 90 million links) and semi-supervised clustering tasks.

In this work, we propose a simple yet effective solution to the problem of connectome inference in calcium imaging data. The proposed algorithm consists of two steps. First, processing the raw signals to detect neural peak activities. Second, inferring the degree of association between neurons from partial correlation statistics. This paper summarises the methodology that led us to win the Connectomics Challenge, proposes a simplified version of our method, and finally compares our results with respect to other inference methods.